2. If A = {1, 2, 3} and B = {2, 3, 4}, and R is the relation on AxB defined by xRy when x + 2y is divisible by 4, then R =

Q: 1. Let S = {1,2, 3, 4}. (a) How many relations are there on S? (b) How many are reflexive? (o) How m…

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Q: 1. Suppose that we have the binary relations R1 C Ax B, R2C B×C, and R3 C C x D. Then the relations…

A: As per the question we are given that the relations : R3 o (R2 o R1) and (R3 o R2) o R1 are…

Q: 2. Define the sets X = {1,2,3} and Y = {4,5,6}. Now, define the relation R from X to Y by „R, if and…

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Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: 9.5. For the relation R= {(1,1),(1,2) , (1, 3) , (2, 2) , (2, 3) , (3, 3)} defined on the set {1,…

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Q: (a) Ri (b) R2= {(1,2), (1,3),(1,4),(2,2),(3,3),(5,3),(5,4),(5,2)} /hich of them is an equivalence…

A: Any relation is equivalence relation if satisfy the following conditions where is set of elements a)…

Q: 1. Suppose that we have the binary relations R1 C Ax B, R2 C B×C, and R3 C C x D. Then the relations…

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Q: Let A = { 2, 3, 4, 6 } and B = { 6, 8, 10 } and define a relation R from A to B as follows: For all…

A: Given that : A = {2, 3, 4,6} and B = {6,8,10} define relation  A*B→R R = {(x ,y): yx is an integer ,…

Q: 1. Suppose that we have the binary relations R1 C A× B, R2 C Bx C, and R3 C C x D. Then the…

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Q: Let Asfl,2,3} and The relations Ri=f(),(2,),(3,2) | find the following Ye lations

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Q: PROBLEM 30. For (x, y) and (u, v) in R2, define (x, y) ~ (u, v) if x² + y² = u? + v?. Prove that…

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Q: 4. Let R be the relation {(1, 2), (1, 3), (2, 3), (2, 4), (3, 1)), and let S be the relation {(2,…

A: To find the composition of two relations R and S . the domain of S°R will be same as domain of R…

Q: If A = {2, 3, 4, 5}, B = {1, 2, 3} then the relation R = { (a, b)|asb} is given by: {(2, 3), (2, 2),…

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Q: that P ◦ Q is an equivalence relation on X iff P ◦ Q = Q ◦ P

A: Concept:

Q: 6f) For the set X = {m,n, p, q,r, s}, let R be a relation on P(X) (the power set of X), given by A R…

A: Yes , this is correct. The set X= {m, n, p, q, r, s} |X|=6 The power set P(X)={ {}, {m}, {n},…

Q: Let A = {0, 1, 3, 5, 7, 8} and R be a relation defined on A such that R= {(x , y)| 4 divdes (x –…

A: We are given the set A = {0, 1, 3, 5, 7, 8} and the relation R defined on A such that R = {(x, y)| 4…

Q: Let A = {0, 1, 2} and B = {0, 8, 9}. If R is the relation from A to B such that (a, b) ∈ R provided…

A: If ab=0 then either a or b is equal to 0 Both also can be 0.

Q: Let A = {0,1,2} and r = {(0,0), (1,1), (2,2 y that r is an equivalence relation on A.

A: The relation is reflexive, since a,a∈R, where a∈A Also, since a=b where (a,b)∈R therefore, the…

Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all (x, y) ∈ A…

A: A=3,4,5B=1,2,3,4R=x,y: x∈A, y∈B ∋xy>7 a. R=3,3, 3,4, 3,5, 4,2, 4,3, 4,5, 5,2, 5,3, 5,4, 5,5

Q: Given the relation R= {(1,1), (2.2), (3.3)(4.4), (1.2). (2.1) (3.4). (4.3)) on the set X- (1,2.3.4).…

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Q: Let A = {3, 4, 5} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: 2. Let R be the relation on the set {1,2,3,4} containing the ordered pairs (1,2), (1,4), (2,1),…

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Q: Given a natural number c ∈ N. The relation Rc is defined as follows: ∀ a, b ∈ N :  (a, b) ∈ Rc ⇔ (∃…

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Q: Let A = {1, 2, 3, 4, 5} and R be the relation defined by a R b if and only if a < b. (a) Compute R²…

A: use the concept of composition          R2=RoR          R3=R2oR

Q: Let A = {9, 11, 12, 14} and B = {1, 2, 3, 4} and define a relation R: A → B as follows: For all…

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Q: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b) : |a –…

A: Given: Show that each of the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12}, given by(i) R = {(a, b)…

Q: Suppose A,S C U, (<) E LOrd(A), and B := (a1, b1), (a2, b2) E (A × B): D(S). If we define a relation…

A: Given A,S⊂A ≤ is the lattice of A. B is the power set of δ , P(S) so if b1,b2 be two subsets of B.…

Q: Given the following relation on {1,2,3,4}, is this relation equivalence? R = {(1,1), (1,3), (1,4),…

A: An equivalence relation on a set is a binary relation that is reflexive, symmetric and transitive.

Q: Given a natural number c ∈ N. On natural numbers, the relation Rc is defined as follows: ∀ a, b ∈ N…

A: (a) let (a,a) be in Rc .      Then there exist integers u and v such that       au + av = c…

Q: y)∈R means that x²-y² is a nonnegative integer. Which of the following is true?     a. 1 R 2 b. 2 R…

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Q: Let A 1, 2} and B = {1, 2, 3} and define a relation R from A to B as follows: Given any (x, y) E A x…

A: Given

Q: If R, T, G,H are relation on A and RET,GCH then, 1. RoG CTOH 2. Тон с RoG 3. RoT S Goн 4. RoH E ToG…

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Q: Show that the relation R on Z defined by aRb if and only if 5a−3b is even, for a, b ∈ Z, is an…

A: Let R be a relation from a set A to itself. R is said to be an equivalence relation if 1) R is…

Q: b. Consider the recurrent relationĄ =24-1 +34-2, where n 22 and Ą =1,4 =2. Compute the next terms…

A: Question 1: Recurrent relation problen is solved.  Solving more than 1 is against the policy of…

Q: 4. Let R be the relation xRy if 3| (x – y) on Z. Prove that R is an equivalence relation.

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Q: Let R be the relation on the set S = {1,2,3, a, b, c} given by xRy if and only if (а, у) € {(а, а),…

A: Given R be the relation on the set S=1,2,3,a,b,c given by…

Q: 1. Suppose that we have the binary relations R1 C Ax B, R2 C B×C, and R3 C C x D. Then the relations…

A: Use the following definitions, to obtain the solution. Let A and B be any two sets. The binary…

Q: 9.15. A relation R is defined on Z by a Rbif |a – b| < 2. Which of the properties reflexive,…

A: Given : A relation is R is defined on Z is given by  a R b if a-b≤2  Which of the properties…

Q: Let S {3k : k E Z} be the set of integer multiples of 3. Let R be a relation defined on Q by x Ry if…

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Q: Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R, S, and T from A to B as follows: For all…

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Q: 1. Suppose that we have the binary relations R1 C A× B, R2 C Bx C, and R3 C C x D. Then the…

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Q: 1. List the ordered pairs in the relation R from A = {0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 1. Let A = {1, 2, 3, 4, 5, 6}. Write out the relation R that expresses | (divides) on A.

A: The relation R that express |(divides) on A is represented by, R={(x,y)| x,yϵA, x|y}

Q: 6) Let A = {1,2,3,4}, show that by counterexamples that the following relations are not equivalence…

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Q: Let A = {#, 7, x} and let R be the relation on A given by R = {(7, 7), (#, #)}

A: R is  said to be reflexive relation on A if for all x in A, xRx holds.  R is said to be symmetric…

Q: the 品|名 Let A = {0, 1, 3, 4, 5, 6} and define the relation R and S on A b) as follows: For every (x,…

A: using the concept of relation ...

Q: Our universe U is Z (integers), and R is the relation defined by R(x,y):=x<y^2 For example,  R(3,-2)…

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Q: Find all equivalence relations on {1,2, 3}.

A: A relation R on a set A is said to be an equivalence relation if it is reflexive symmetric and…

Q: If R = {(1,2),(2,1),(2,2),(3,4)} is a relation on the set {1,2,3,4}.The reflexive closure of R is :

A: Given that R=1,2,2,1,2,2,3,4 is a relation on a set 1,2,3,4  Consider A=1,2,3,4